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The No.2-seeded Vinci was the first to advance, losing the first game of the match but then taking 12 in a row to beat Karolina Pliskova, 61 60. It wasn't as lopsided as the scoreline made it look - Pliskova had game points in four of those 12 games, and two of those games were marathons, one going to seven deuces and the other six - but Vinci beat the Czech wildcard to the finish line every time.
"I played great today," Vinci said after the match. "I expected a very tough match today and it was better than that, but everything in my game was just perfect on the court. Now I'm just happy I'm in the semifinals and I'm very much looking forward to playing again in the semifinals tomorrow."
Vinci fought off all five break points Pliskova got during the match - but there is a number that might have gotten under Vinci's skin a bit, that she only converted six of her own 20 break points.
The next match saw Beck take on Maria Elena Camerin, and things looked like they were swinging heavily in Camerin's favor early on, as she raced out to a 5-1 lead - Beck clawed her way back into the match, though, winning five games in a row and eventually cruising in the first set tie-break, then was crushing in the second set, easing to victory in straights against the Italian qualifier, 76(1) 60.
Beck is now through to her first WTA semifinal. She was a point away from achieving this earlier this year at Shenzhen - she held match point against Peng Shuai before falling in the quarterfinals there - but this time she converted on her very first match point to break into her first WTA semifinal.
"When I was down today I just had to stay cool, play more rallies and let her do the work - and forget I was playing for the semifinals of a WTA tournament!" Beck said. "I tried to keep that out of my mind and it worked out. And I didn't expect to reach the semifinals here at the beginning of the week because everyone here is such a good player - so many Top 100. I'm very happy to reach the semis."
Beck was asked about the transition from juniors and ITFs to the WTA circuit. "It's a big step," she said. "The players you play in the finals of ITFs are the ones you play first round in the WTAs, so you know it's going to be tougher. You have to improve all the time and take your chances against everyone."
Meanwhile, Vinci will be playing the 18th WTA semifinal of her career, going 8-9 in her first 17 - and of those eight times she won, she went on to capture the title a very impressive seven times.
Beck's match against the No.13-ranked Vinci will be her first time playing a Top 20 player. But in her only two previous matches against Top 30 players she prevailed, beating then-No.25 Hsieh Su-Wei in Shenzhen this year and then-No.28 Yaroslava Shvedova at the Australian Open, also this year.
"It's a very good feeling to play the semis tomorrow against Roberta Vinci," Beck said. "She's No.1 in doubles and a Top 20 player in singles, so I'll enjoy it. I'll really have to play my best tennis."
Vinci and Beck will be playing against each other for the first time.